Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity. (English. Russian original) Zbl 1362.35069

Comput. Math. Math. Phys. 56, No. 7, 1355-1362 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 7, 1363-1370 (2016).
Summary: Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.


35C06 Self-similar solutions to PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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